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Reference: Pearson Edexcel International A Level Pure Mathematics 3 Student Book. This chapter expands trigonometry using reciprocal functions and inverse trigonometric functions.
Main skills from this lesson
The three reciprocal trigonometric functions are:
They are undefined when their denominator is zero.
sec x cos x = 1 cosec x sin x = 1 cot x tan x = 1
Always ask: where is the denominator zero? Those x-values are not allowed.
Reciprocal trig graphs often have vertical asymptotes. These happen where the original sin, cos or tan value is zero.
A good sketch should show:
Do not draw a reciprocal graph crossing its vertical asymptote.
Build identities from sin^2 x + cos^2 x = 1.
Divide by cos^2 x:
1 + tan^2 x = sec^2 x
Divide by sin^2 x:
cot^2 x + 1 = cosec^2 x
These are useful for simplifying and solving equations.
1 + tan^2 x = sec^2 x 1 + cot^2 x = cosec^2 x
Inverse trig functions return angles. Because normal trig functions repeat, inverse trig needs restricted ranges.
Study tip:
Continue with quizzes, flashcards, or games when you are ready.